INTRODUCTION

We are planning to have an 'End Of Term' party in our classroom.

• It's our job to make sure that every student has a one table setting made up of exactly:
  1. one cup
  2. one bowl
  3. one plate

Each of the table setting (each combination of cups, bowls & plates) must be different:

• Each setting must have at least one item colour that makes it different to every other setting.

Your teachers will choose students to work in three teams of ten (depending on class size).

• Each team will need to have ten or more of each item (in whatever colours are specified below) to build place settings.

Fig 1. The cup, plate and bowl in the above image are just an example only

Write the date and the title 1. Cups, Bowls and Plates on a clean page in your journal.

Make a prediction of the number of different settings you think you can make using.

• CUPS of three colours: RED, WHITE, BLUE.
• BOWLS of two colours: RED, WHITE
• You have NO plates

Working together, make as many settings of different colour combinations as you can.

Write down your prediction and draw a circle around the number.

Write down how many settings that you made and convince each-other that you have found all of the possible settings (that there are no more or no less). Draw a square around the number that you found.

Write the date and the title 2. Cups, Bowls and Plates on a clean page in your journal.

Divide into three groups - no more than ten students in each group.

You will be given ten cups, ten bowls for each of the following colours:

• CUPS: RED, WHITE, BLUE
• BOWLS: RED, WHITE
• PLATES: WHITE

Make a prediction of the number of settings of different colour combinations that you think your team can now make:

1. Write down your prediction and draw a circle around the number.
2. Working together, make as many settings as you can make using different colour combinations.

Write down how many settings that you made and convince each-other that you have found all of the possible settings (that there are no more or no less possible colour combinations).

Draw a square around the number that you found.

Each group will be given ten extra plates of a new colour (RED)

You will now have ten cups, ten bowls and ten plates for each of the following colours:

• CUPS: RED, WHITE, BLUE
• BOWLS: WHITE. RED
• PLATES: RED, WHITE

Is it possible for 10 children at the party to each have a different colour combination of one cup, one bowl and one plate?

Write down your prediction and draw a circle around it.

Convince others that you have found all of the possible combinations.

Write down how many combinations that you found, and then draw a circle around your answer

Is it possible for 15 children at the party each to have a different combination of cup, bowl and plate?

Write down your prediction and draw a circle around it.

What is the smallest number of different colours would you need for:

1. CUPS = (how many colours)?
2. BOWLS = (how many colours)?
3. PLATES = (how many colours)?

Write down your prediction and draw a circle around the number.

Convince your team that you have found all of the possible settings (that there are no more or no less). Draw a square around the number that you found using your solution.

Planning Your 'End Of Year Class Party'

Is it possible for 30 children at the party each to have a different colour combination of cup, bowl and plate?

How many items of each colour do we need so that we can give every student in our class a place at the party if we give them each one cup, one bowl and one plate?

Write down your prediction and for 'number of colours' and 'number of items' - Draw a circle around these numbers.

Compare & Justify Your Solutions With Your Group/Class.